Yes, using query parameters:
Restrict the user custom fields to search by modifying the last parameter user_field_ids=1|2
.
For example, user_field_ids=5
to search only in the custom field ID 5.
There are also a couple of other available parameters you can find in the API documentation (docs that don’t mention the user fields, but you can easily reverse-engineer the API.
The custom field(s) must have the searchable option checked for the query to work:
Also, note that the query will not search only in custom fields, but also in usernames and maybe full names. I think there’s no built-in feature to filter only by custom fields.